No, you are correct. The FSF does not consider search engines SaaS
(http://www.gnu.org/philosophy/who-does-that-server-really-serve.html)
See the section on "Distinguishing SaaS from Other Network Services"
"Services such as search engines collect data from around the web and let you
examine it. Looking through their collection of data isn't your own computing
in the usual sense—you didn't provide that collection—so using such a
service to search the web is not SaaS. (However, using someone else's search
engine to implement a search facility for your own site is SaaS.)"
